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If 3 + 5 =5, then 5 -3 is equal to

Question

If $3 sin θ + 5 cos θ = 5$ , then $5 sin θ - 3 cos θ$ is equal to

3

8

13

none of these

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Emma Discussed

3 sin θ + 5 cos θ = 5

, then

5 sin θ - 3 cos θ

is equal to

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

Given

3 s in θ + 5 cos θ = 5

Squaring both sides, we get

9 sin^{2} θ + 25 cos^{2} θ + 30 sin θ cos θ = 25

\Rightarrow 9 - 9 cos^{2} θ + 25 - 25 sin^{2} θ + 30 sin θ cos θ = 25

\Rightarrow 9 cos^{2} θ + 25 sin^{2} θ - 30 sin θ cos θ = 9

\Rightarrow (5 sin θ - 3 cos θ)^{2} = 9

\Rightarrow 5 sin θ - 3 cos θ = \pm 3

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Question Text	If $3 sin θ + 5 cos θ = 5$ , then $5 sin θ - 3 cos θ$ is equal to
Answer Type	Text solution:1
Upvotes	151